sudoku_rules

nums(1..9).
row(N) :- nums(N).
col(N) :- nums(N).

9 { cell(R, 1..9, 1..9) } 9 :- row(R).
9 { cell(1..9, C, 1..9) } 9 :- col(C).

:- row(R), nums(N), cell(R, Ca, N), cell(R, Cb, N), Ca!=Cb.
:- col(C), nums(N), cell(Ra, C, N), cell(Rb, C, N), Ra!=Rb.
:- row(R), col(C), nums(Na), nums(Nb), cell(R, C, Na), cell(R, C, Nb), Na!=Nb.

cellSum(1, S) :- S = #sum { N : cell(1..3, 1..3, N) }.
cellSum(2, S) :- S = #sum { N : cell(4..6, 1..3, N) }.
cellSum(3, S) :- S = #sum { N : cell(7..9, 1..3, N) }.
cellSum(4, S) :- S = #sum { N : cell(1..3, 4..6, N) }.
cellSum(5, S) :- S = #sum { N : cell(4..6, 4..6, N) }.
cellSum(6, S) :- S = #sum { N : cell(7..9, 4..6, N) }.
cellSum(7, S) :- S = #sum { N : cell(1..3, 7..9, N) }.
cellSum(8, S) :- S = #sum { N : cell(4..6, 7..9, N) }.
cellSum(9, S) :- S = #sum { N : cell(7..9, 7..9, N) }.
:- cellSum(_, AnyCellSum), AnyCellSum!=45.

#show cell/3.

% append games below